Question

A equação log 3 na base x = 1 + log 9 na base x , tem duas raizes iguais , determine o produto dessas raizes .

Answer 1

$\log_x3=1+\log_x9\\\\\log_x3=1+\log_{x}(3\cdot3)\\\\\log_x3=1+\log_x3+\log_x3\\\\log_x3=1+2\cdot\log_x3\\\\1+2\cdot\log_x3-log_x3=0\\\\1+\log_x3=0\\\\\log_x3=-1\ \therefore \ x^{-1}=3\\\\x=3^{\frac{1}{-1}}\\\\x=3^{-1}\\\\x=\dfrac{1}{3}\\\\\\\boxed{S=\left\{\dfrac{1}{3}\right\}}$